Related papers: On the Observability of Gaussian Models using Disc…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…
We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
A joint characterisation of the observability and controllability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
We present Density-Sampled Gaussians (DeG), a novel 3D representation designed to bridge the gap between adaptive rendering primitives and scalable generative modeling. Unlike existing approaches that constrain 3D Gaussians to fixed voxel…
Inspired by the analysis of variance (ANOVA) decomposition of functions we propose a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption that the function we wish to approximate can be well explained…
We study an unbiased estimator for the density of a sum of random variables that are simulated from a computer model. A numerical study on examples with copula dependence is conducted where the proposed estimator performs favourably in…
A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete…
We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…